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# Point (1, 0) is closest to which of the following lines? y =

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Current Student
Joined: 11 May 2008
Posts: 552
Point (1, 0) is closest to which of the following lines? y = [#permalink]

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26 Aug 2008, 10:54
Point (1, 0) is closest to which of the following lines?

y = x
y = 1
y + x = 3
x = 2
x + y = -1

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SVP
Joined: 07 Nov 2007
Posts: 1759
Location: New York
Re: coordinate geometry [#permalink]

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26 Aug 2008, 11:05
arjtryarjtry wrote:
Point (1, 0) is closest to which of the following lines?

y = x
y = 1
y + x = 3
x = 2
x + y = -1

A) y=x

Draw the lines in X-Y co-ordinate.

y = 1,x=2 lines are 1 unit away from (1, 0)
y + x = 3 , x + y = -1 are more than 1 unit away

draw perpendicular line which touchs the line y=x
distance is $$1/sqrt(2)$$
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Last edited by x2suresh on 26 Aug 2008, 11:18, edited 1 time in total.
Manager
Joined: 15 Jul 2008
Posts: 205
Re: coordinate geometry [#permalink]

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26 Aug 2008, 11:05
arjtryarjtry wrote:
Point (1, 0) is closest to which of the following lines?

y = x
y = 1
y + x = 3
x = 2
x + y = -1

use the general formula. given line ax+by+c=0 and point (m,n), the perpendicular distance is
|am+bn+c|/sqrt(a^2 + b^2).

in this case, A seems to be the answer. Didnt calculate, so i could be wrong.
Senior Manager
Joined: 09 Oct 2007
Posts: 459
Re: coordinate geometry [#permalink]

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26 Aug 2008, 11:07
I'd go for A.

Point 1,0 is 1/2sqrt2 from equation in A.
Manager
Joined: 15 Jul 2008
Posts: 205
Re: coordinate geometry [#permalink]

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26 Aug 2008, 11:08
x2suresh wrote:
arjtryarjtry wrote:
Point (1, 0) is closest to which of the following lines?

y = x
y = 1
y + x = 3
x = 2
x + y = -1

A) y=x

Draw the lines in X-Y co-ordinate.

y = 1,x=2 lines are 1 unit away from (1, 0)
y + x = 3 , x + y = -1 are more than 1 unit away

draw perpendicular line which touchs the line y=x
distance is $$1/sqrt(3)$$

I think it should be 1/sqrt(2). coefficients of x and y would come into play. And both coefficients are 1.
SVP
Joined: 07 Nov 2007
Posts: 1759
Location: New York
Re: coordinate geometry [#permalink]

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26 Aug 2008, 11:17
bhushangiri wrote:
x2suresh wrote:
arjtryarjtry wrote:
Point (1, 0) is closest to which of the following lines?

y = x
y = 1
y + x = 3
x = 2
x + y = -1

A) y=x

Draw the lines in X-Y co-ordinate.

y = 1,x=2 lines are 1 unit away from (1, 0)
y + x = 3 , x + y = -1 are more than 1 unit away

draw perpendicular line which touchs the line y=x
distance is $$1/sqrt(3)$$

I think it should be 1/sqrt(2). coefficients of x and y would come into play. And both coefficients are 1.

you are right it should be $$1/sqrt(2)$$ .. typo
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Smiling wins more friends than frowning

VP
Joined: 05 Jul 2008
Posts: 1369
Re: coordinate geometry [#permalink]

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12 Mar 2009, 15:17
bhushangiri wrote:
arjtryarjtry wrote:
Point (1, 0) is closest to which of the following lines?

y = x
y = 1
y + x = 3
x = 2
x + y = -1

use the general formula. given line ax+by+c=0 and point (m,n), the perpendicular distance is
|am+bn+c|/sqrt(a^2 + b^2).

in this case, A seems to be the answer. Didnt calculate, so i could be wrong.

Is there any other way to determine the perpendicular distance from a point to a line?

x2suresh,

How were you calculating the perpendicular distance from a point to a line? Were you using the same formula?
SVP
Joined: 07 Nov 2007
Posts: 1759
Location: New York
Re: coordinate geometry [#permalink]

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12 Mar 2009, 17:36
icandy wrote:
bhushangiri wrote:
arjtryarjtry wrote:
Point (1, 0) is closest to which of the following lines?

y = x
y = 1
y + x = 3
x = 2
x + y = -1

use the general formula. given line ax+by+c=0 and point (m,n), the perpendicular distance is
|am+bn+c|/sqrt(a^2 + b^2).

in this case, A seems to be the answer. Didnt calculate, so i could be wrong.

Is there any other way to determine the perpendicular distance from a point to a line?

x2suresh,

How were you calculating the perpendicular distance from a point to a line? Were you using the same formula?

I did it in different way.

slope of line y=x is 1
slop of line perpendicular to y=x is -1

y = -x +c -->perpendicular line .. which passes through (1,0)
--> c=1

y=-x +1 -->(2)
y=x -->(1)
find the intersection point (1) and (2) --> (1/2,1/2)

distance between (1/2,1/2) and (1,0) --> 1/sqrt(2)
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Intern
Joined: 07 Feb 2009
Posts: 47
Re: coordinate geometry [#permalink]

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14 Mar 2009, 01:06
The closest line i found is y=x. i.e A should be the answer.
Also the distance from y=x to the point (1,0) is 1/sqrt(2).

To find the distance from y=x, draw a line parallel to y=x which passes from (1,0).
Parallel line would be y=-x+c and as it passes from (1,0) we get c=1.
0=-1+c --> c=1
so the parallel line is y=-x+1.
as these two equations cross each other, we find out the point of intersection.
Using equations y=x and y=-x+1, we get (1/2,1/2) as the point of intersection.

now distance from point (1,0) to the point (1/2,1/2) = sqrt((1-1/2)^2+(0-1/2)^2) = 1/sqrt(2).
VP
Joined: 28 Dec 2005
Posts: 1499
Re: coordinate geometry [#permalink]

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15 Mar 2009, 15:54
Here's maybe a silly question, but what i remember from back in school was the distance between two points was given by the formula here:

http://www.purplemath.com/modules/distform.htm

So for y=x, the point would be (1,1), and the distance from there to the point (1,0) would be 1 wouldnt it ?? Where have I misunderstood ?
Manager
Joined: 02 Mar 2009
Posts: 129
Re: coordinate geometry [#permalink]

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15 Mar 2009, 23:11
I like bhushangiri's formula the best although for this question you dont really have to do any calculations. You can draw the axis and see approximate perpendicular distances of the point from the line.

Thanks.
Manager
Joined: 14 Nov 2008
Posts: 188
Schools: Stanford...Wait, I will come!!!
Re: coordinate geometry [#permalink]

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16 Mar 2009, 07:01
if you plot it on the graph, it will be very clear that y=x is the closest to the point. and is 1/srrt 2 distance away perpendicularly.

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: coordinate geometry   [#permalink] 16 Mar 2009, 07:01
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# Point (1, 0) is closest to which of the following lines? y =

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